One form of apparatus for coating objects comprises transport means for transporting the object through treatment stations along a transport path which is linear at least on a portion of its extent, as disclosed in U.S. Pat. No. 6,082,256. Therein the transport means include screws for transporting the objects, each of which is positioned on a carriage-like holding device which is moved through the treatment stations by the screw along a particular guide configuration. That arrangement is distinguished by precise orientation of the objects to be printed upon, in relation to each respective printing mechanism, so that even in the case of multi-color printing in which a plurality of partial print images are successively applied to the object and there combine together to form an overall print image, it is possible to achieve excellent print image quality.